Find the equation of the line that passes through a point and is contained on a cylinder I need to find the vector equation of the line that passes through the point (5,0,5) and is contained on the elliptic cylinder given by $\frac{x^2}{5^2}+\frac{y^2}{4^2}=1 $ I know I only have to find the vector of the direction of the cylinder's generatrix that passes through the point, but I don't understand how

The point $(5,0,5)$ lies on the elliptic cylinder.

$\mathbf{r}(t)=(5,0,0)+t(0,0,1)$ is a line which lies on the elliptic cylinder and passes through this point.